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On Monday, August 22, 2005 8:20 AM Martin Rubey wrote:

In private communication, we developed the domain below, but your idea is conceptually better, I think. The full blown thing would then be a category Units, that has as domains Mass, Time, Length, ... I suppose.

)abbrev domain UNITS Units
Units(R: Field): Exports == Implementation where
U == Fraction Polynomial Integer
Exports == with
"*": (%,%) -> %
"+": (%,%) -> %
coerce: % -> OutputForm
withUnits: (R, U) -> %
setUnitSystem!: String -> String
Implementation == add Rep := Record(expr: R, units: U)
system: String := "MKS" setUnitSystem! s == t := system system := s t
transform: U -> Record(scalar: R, units: U)
transform u == m := 'm::Symbol::Polynomial(Integer)::U v := u if system = "MKS" then v := eval(u, ['cm, 'dm], _ [m*1/100::U, m*1/10::U])$RationalFunction(Integer) s: Fraction Integer := leadingCoefficient(numer(v)) _ / leadingCoefficient(denom(v)) r: U := leadingMonomial(numer(v))::U _ / leadingMonomial(denom(v))::U _ / s ::U [s::R, r] withUnits(e, u) == [e, u]::Rep x * y == [(x::Rep).expr * (y::Rep).expr, (x::Rep).units * (y::Rep).units] x + y == ux := transform((x::Rep).units) uy := transform((y::Rep).units) if ux.units = uy.units then [(x::Rep).expr*ux.scalar + (y::Rep).expr*uy.scalar, ux.units] else error "+: Units have to match" coerce x == coerce((x::Rep).expr)$R * coerce((x::Rep).units)$U spad Compiling FriCAS source code from file /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/884360936492130004-25px001.spad using old system compiler. UNITS abbreviates domain Units ------------------------------------------------------------------------ initializing NRLIB UNITS for Units compiling into NRLIB UNITS compiling exported setUnitSystem! : String -> String Time: 0.02 SEC. compiling local transform : Fraction Polynomial Integer -> Record(scalar: R,units: Fraction Polynomial Integer) Time: 0.05 SEC. compiling exported withUnits : (R,Fraction Polynomial Integer) ->$ UNITS;withUnits;RF$;3 is replaced by CONS Time: 0 SEC. compiling exported * : ($,$) ->$ Time: 0.01 SEC.
compiling exported + : ($,$) -> $Time: 0 SEC. compiling exported coerce :$ -> OutputForm Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |Units| REDEFINED
;;; *** |Units| REDEFINED Time: 0 SEC.
Warnings: [1] *: expr has no value [2] *: units has no value [3] +: units has no value [4] +: expr has no value [5] +: scalar has no value [6] coerce: expr has no value [7] coerce: units has no value
Cumulative Statistics for Constructor Units Time: 0.08 seconds
finalizing NRLIB UNITS Processing Units for Browser database: --->-->Units(constructor): Not documented!!!! --->-->Units((* (% % %))): Not documented!!!! --->-->Units((+ (% % %))): Not documented!!!! --->-->Units((coerce ((OutputForm) %))): Not documented!!!! --->-->Units((withUnits (% R (Fraction (Polynomial (Integer)))))): Not documented!!!! --->-->Units((setUnitSystem! ((String) (String)))): Not documented!!!! --->-->Units(): Missing Description ; compiling file "/var/aw/var/LatexWiki/UNITS.NRLIB/UNITS.lsp" (written 04 APR 2022 05:50:09 PM):
; /var/aw/var/LatexWiki/UNITS.NRLIB/UNITS.fasl written ; compilation finished in 0:00:00.036 ------------------------------------------------------------------------ Units is now explicitly exposed in frame initial Units will be automatically loaded when needed from /var/aw/var/LatexWiki/UNITS.NRLIB/UNITS

For example:

fricas
x:=withUnits(2.1,m)
 (1)
Type: Units(Float)
fricas
y:=withUnits(3.2,s)
 (2)
Type: Units(Float)
fricas
x*y
 (3)
Type: Units(Float)
fricas
z:=withUnits(z::Polynomial Float,kg)
 (4)
Type: Units(Fraction(Polynomial(Float)))
fricas
z*z
 (5)
Type: Units(Fraction(Polynomial(Float)))

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